what is answer??????????????????

I think that the problem is supposed to say that "square of the difference of the 4th and the 1st term is 225"  rather than 255......when I tried 255 I get a strange square root which doesn't allow for any "integer" answers [If I didn't make a mistake, that is !!!!].....I'm working this one assuming 225 is correct...

The first term is just a1

Let the 4th  term be given by:

a4 = a1 + d(4 -1)   =  a1 + 3d

And the difference between the 4th and 1st terms is just 3d

And the square of this difference  = 225

So  (3d)^2  = 225 →  9d^2 = 225  →  d^2  = 225/9  →   d =  15/3   so d =5 [since all the terms are positive]

And we're told that    [ (a1 + d(7) ) - (a1 + d(3)) ] / [a1 + d (14) ]  = 4/15  simplify   

[d(7) - d(3)] /[ a1 + d(14)] = 4/15   and sustituting 5  for d we have

[5(7) - 5(3)] /[ a1 + 5(14)] = 4/15

5*4  = [4/15]  (a1 + (5)*14)     multiply through by 15

5*4*15 = 4[a1 + 70]

300 = 4a1 + 280

20 = 4(a1)

So a1  = 5

So

2015 = 5 + 5(n -1)

2010 = 5(n -1)

402 = n - 1    add 1 to both sides

403    which is answer "3"